Question

Solve the system using elimination by addition.

x + y + z = 0
-x + y - 2z = 6
2x + y + z = 0

Answer 1

If the first equation is subtracted from the third equation the result is x = 0. The equations then reduce to

y + z = 0
y - 2z = 6
y + z = 0 (which is just a copy of the first equation)

If we multiply the first equation by 2 and add it to the second equation we get 3y = 6 or y = 2. And that forces z = -2.